pi0 (version 1.3-250)

nparncpt: Nonparametric estimation of noncentrality parameters

Description

The functions use Gaussian basis functions to estimate the noncentrality parameters (ncp) from a large number of t-statistics.

Usage

nparncpt(tstat, df, ...)
nparncpt.sqp(tstat, df, penalty=c('3rd.deriv','2nd.deriv','1st.deriv'), lambdas=10^seq(-1,5,by=1), 
        starts, IC=c('BIC','CAIC','HQIC','AIC'), K=100, bounds=quantile(tstat,c(.01,.99)), 
        solver=c('solve.QP','lsei','ipop','LowRankQP'),plotit=FALSE, verbose=FALSE, approx.hess=TRUE, ... )

Arguments

tstat

Numeric vector of noncentrality parameters

df

Numeric vector of degrees of freedom

penalty

Character vector. Penalty on either integrated squared first-order derivatives (1st.deriv) or second-order derivatives (2nd.deriv) of the estimated density function of ncp. Note that only the first element is used.

lambdas

Numeric vector of smoothness tuning parameter lambda to be tried. The one that minimizes NIC will be chosen.

starts

Optional numeric vector of starting values. If missing, parncpt will be called with zeromean set to FALSE to get an initial esimate of pi0. And the starting values (theta) will be set all

IC

Character; one of AIC, BIC, CAIC, HQIC, specifying the factor multiplied to the ENP in computing Information Criterion (IC).

K

The number of basis Gaussian density functions.

bounds

A numeric vector of length 2, giving the approximate bounds where most of the probability of ncp lies.

solver

Character. The name of the function for solving quadratic programming problems. Note that ipop and kernlab are not very reliable. solve.QP is faster but lsei is more stable.

plotit

logical; indicating if plot.nparncpt should be called after estimation. This is always recommended before accepting the results.

verbose

logical; if TRUE, extensive messages will be printed.

approx.hess

either logical or a number between 0 and 1. This helps in reducing time in evaluating the hessian matrix. If it is set to TRUE, for the kth Gaussian basis function and the gth tstat, the marginal t-statistic density evaluated

...

other paramters passed to dtn.mix. Usually, the approximation argument.

Value

• A list with class attribute c("nparncpt", "ncpest")
• pi0
  estimated proportion of true nulls
• mu.ncp
  mean of ncp
• sd.ncp
  SD of ncp
• logLik
  an object of class logLik. The associated df is the estimated effective number of parameters (enp). The log likelihood is also penalized likelihood. See also logLik.ncpest and AIC.
• enp
  estimated ENP
• par
  estimated parameters theta
• lambda
  the lambda that minimizes NIC
• gradiant
  analytic gradiant at the estimate
• hessian
  analytic hessian at the estimate
• beta
  estimated mixing proportions for the NCP distribution
• IC
  the information criterion specified by the user
• all.mus
  mean of each basis Gaussian density
• all.sigs
  SD of each basis Gaussian density
• data
  a list of tstat and df
• i.final
  the index of lambdas that minimizes NIC
• all.pi0s
  estimated pi0 for each lambda
• all.enps
  ENP for each lambda
• all.thetas
  parameter estimates for each lambda
• all.nics
  Network information criterion (NIC) for each lambda
• all.nic.sd
  SD of NIC for each lambda
• all.lambdas
  the lambdas argument itself

Details

nparncpt is a wrapper for nparncpt.sqp, the latter of which uses a sequential quadratic programming algorithm to find the mixing proportions of the basis Gaussian density functions.

References

Qu L, Nettleton D, Dekkers JCM. (2012) Improved Estimation of the Noncentrality Parameter Distribution from a Large Number of $t$-statistics, with Applications to False Discovery Rate Estimation in Microarray Data Analysis. Biometrics (in press).

See Also

parncpt, sparncpt, fitted.nparncpt, plot.nparncpt, summary.nparncpt, coef.ncpest, logLik.ncpest, vcov.ncpest, AIC, dncp

Examples

data(simulatedTstat)
(npfit=nparncpt(tstat=simulatedTstat, df=8)); 
(pfit=parncpt(tstat=simulatedTstat, df=8, zeromean=FALSE)); plot(pfit)
(pfit0=parncpt(tstat=simulatedTstat, df=8, zeromean=TRUE)); plot(pfit0)
(spfit=sparncpt(npfit,pfit)); plot(spfit)